I indeed have several examples of such situations, where a consultant is contacting you (on behalf of HR) to answer your question.
The purpose is for you to gather the information you would like to learn about the firm before the formal interviews, and for them to quickly check that you will fit (at least no counter order).
1. Yes, depending on the firm it happens, specially for experienced hire
2. Ask questions about the firm current business (what industries, types of jobs, etc), culture (how the integration of experienced hire works ) and opportunities (training, exposure)
3. Be Ready to quickly introduce yourslef and the reasons of you rmove to consulting and more specifically to the targgeted firm
Hope this helps